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Symmetric error estimates for discontinuous Galerkin time-stepping schemes for optimal control problems constrained to evolutionary Stokes equations

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  • Konstantinos Chrysafinos
  • Efthimios Karatzas

Abstract

We consider fully discrete finite element approximations of a distributed optimal control problem, constrained by the evolutionary Stokes equations. Conforming finite element methods for spatial discretization combined with discontinuous time-stepping Galerkin schemes are being used for the space-time discretization. Error estimates are proved under weak regularity hypotheses for the state, adjoint and control variables. The estimates are also applicable when high order schemes are being used. Computational examples validating our expected rates of convergence are also provided. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Konstantinos Chrysafinos & Efthimios Karatzas, 2015. "Symmetric error estimates for discontinuous Galerkin time-stepping schemes for optimal control problems constrained to evolutionary Stokes equations," Computational Optimization and Applications, Springer, vol. 60(3), pages 719-751, April.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:3:p:719-751
    DOI: 10.1007/s10589-014-9695-3
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    References listed on IDEAS

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    1. Andreas Springer & Boris Vexler, 2014. "Third order convergent time discretization for parabolic optimal control problems with control constraints," Computational Optimization and Applications, Springer, vol. 57(1), pages 205-240, January.
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